Currently, millions of objects remain buried worldwide ranging from small-sized land mines to large-size waste disposal and storage drums. Presently over 10,000 suspected contaminated sites at current and former United States Department of Defense (DoD) installations are coming under remediation and reclamation. These sites contain everything from a motor pool, laundry or landfill, to an array of abandoned-ordnance. The task of reclaiming lands filled with mines, ammunition, and chemical wastes is far from simple.
In addition, techniques to locate, identify and characterize buried objects such as reinforcing bars (rebars), fibers and cracks in concrete structures, composite materials, and other metallic and non-metallic structures are in great demand. The most useful techniques are those that can locate, identify and characterize buried objects in real time. Similarly, in biological systems, techniques that can provide conductivity profile of the interior of a body, object or system are of great commercial and technological importance.
Various methods have been developed to detect buried objects. These methods include electromagnetic and magnetometer sensors, ground penetrating radar, infrared, and several types of chemical and spectroscopic tools.
Subsurface conductivity measurements, sometimes termed conductivity-tomography or electrical impedance-tomography, have been reported in the published literature since the late 1970s (see B. H. Brown, D. C. Barber, Wei Wang, Liquin Lu, A. D. Leathard, R. H. Small wood, A. R. Hampshire, R. Mackay, and K. Hatzigalanis, 1994, xe2x80x9cMulti-Frequency Imaging and Modeling of Respiratory Related Electrical Impedance Changes,xe2x80x9d Physiol. Meas., Vol. 15, A1-A12; R. D. Cook, G. J. Saulnier, D. G. Gisser, J. C. Goble, J. C. Newell and D. Isaacson, 1994, xe2x80x9cACT3: A High-Speed, High-Precision Electrical Impedance Tomograph,xe2x80x9d IEEE Trans. Biomed. Eng., Vol. 41, No. 8, pp. 713-722, and references therein; and R. W. Smith, I. L. Freeston, and B. H. Brown, 1995, xe2x80x9cA Real-Time Electrical Impedance Tomography System for Clinical Usexe2x80x94Design and Preliminary Results,xe2x80x9d IEEE Trans. Biomed. Eng., Vol. 42, No. 2, pp. 133-140, and references therein). These measurements have been widely used in mapping the internal conductivity of biological bodies, as well as geological sites. These techniques involve placing electrodes around the sites with objects under investigation, and sending a known amount of electrical current through the site. The current generates electrical potentials or fields that are measured using another set of electrodes placed on that surface. Next, the internal conductivity of the object is reconstructed using the measured potential values, injected current, and the location of the electrodes.
Several types of mathematical reconstruction algorithms have been used and reported since 1970s (see B. H. Brown, D. C. Barber, A. H. Morice, and A. D. Leathard, 1994, xe2x80x9cMulti-Frequency Imaging and Modeling of Respiratory Related Electrical Impedance Changes,xe2x80x9d IEEE Trans. Biomed. Eng., Vol. 41, No. 8, pp. 729-733; Smith et al., 1995; and A. Wexler, B. Fry and M. R. Neuman, 1985, xe2x80x9cImpedance-Computed Tomography Algorithm and System,xe2x80x9d Applied Optics, Vol. 24, No. 23, pp. 3985-3993). Most of these techniques have attained a certain level of qualified success. Using these techniques the subsurface conductivity can be mapped 1) when the differences between the conductivity values of the site elements and objects are small; and 2) when the internal gradients of the potentials can accurately be calculated (Cook et al., 1994).
However, none of these techniques has been successful in locating of plastic or metal mines buried at shallow depths. Objects buried under surfaces tend to have widely varying electrical properties. Furthermore, accuracy in the potential measurements often cannot be assured. In addition, the current and potential data are likely to be corrupt with noise in the field, and measurement of distances between the locations of electrodes is also subject to uncertainties. Under such restricted conditions of the field, reconstructing conductivity values obtained using conventional gradient-base techniques (see Brown et al., 1994, and Smith et al., 1995) may not be truly representative of the subsurface structure and contents. For these reasons, locating small-sized objects such as mines through conductivity measurements has so far remained largely unsuccessful.
The invention is directed to an apparatus and method for locating objects in a body through the mapping and imaging of the conductivity profiles of such objects by applying a force to the object and/or body and measuring certain characteristics of the body responsive to the application of force. In accordance with a preferred embodiment, the force applied to the object and body is in the form of an electrical voltage or current such that electrical potential, currents, and magnetic fields are generated throughout the subsurface site. The voltage, current, or magnetic field is then measured at the surface, above the surface or at the boundary of the body. A global stochastic approximation technique, modified simultaneous perturbation stochastic approximation (SPSA), is then used to estimate the subsurface conductivity and the locations of the objects by minimizing a loss function. The loss function is formed from the total errors between the measured values from sensors and the computed values from the conductivity profile and the locations of the objects by finite element method (FEM). The object locations and conductivities identify the object types and their material composition. There are two distinct components to the approach, one is the use of a modified SPSA; another is estimation of the location and conductivity of the objects in conjunction with the conductivity profile of the finite element model.
The invention differs from others (for example, xe2x80x9cElectrical Resistance Tomography for Imaging the Spatial Distribution of Moisture in Pavement Sectionsxe2x80x9d by M. Bultnev, A. Ramirez, and W. Dailyxe2x80x9d in Proceedings of the Structural Materials Technology: an NDT Conference, Eds: P. E. Hartbower and P. J. Stolarski, February 1996, San Diego, p. 342 ) in several ways. 1. It uses magnetic field measurements from above surface, and potential (voltage) measurements from the soil surface. 2. It can be operated with either magnetic field measurements only, or the potential measurements only. 3. This invention uses a modified SPSA gradient approximation algorithm as compared with conventional numerical gradient algorithms used by others. 4. The modified SPSA algorithm avoids ambiguities and uncertainties in the field setting. 5. Use of the modified SPSA to estimate the finite element model for the subsurface and the locations and the conductivities of the objects help characterize objects that are smaller than the size of the elements in the finite element model.